Thermodynamics of Finite Systems and the Kinetics of First-Order Phase Transitions

This booklet is devoted to the thermodynamic and kinetic description of first-order phase transitions. In general, the matter of the world exists in different phases. Normally phase ctlanges take place in ther­ modynamic equilibrium, which will be considered here. Typically,the system is rapidly quenched from a one-phase thermal equilibrium state to a nonequilibrium situation. During the so-ca lIed equilibrium phase transformation process the quenched supersaturated system evolves from the nonequilibrium state to an equilibrium one which consists of two coexisting phases. In aseries of books on phase transitions and critical phenomena (DDMB, GREEN, lEBDWITZ, 1972 - 19B3) an immense amount of material to different aspects of ttlis topic is summarized. The other type of phase transitions takes place in systems far from equilibrium. Due to 'the nonequi1ibrium boundary conditions and the flu­ xes from the environment into the system the final state of this so­ called nonequilibrium phase transition is a stable nonequilibrium si­ tuation. Such interesting processes (e. g. pattern formation, multista­ bi1ity) do not appear only in physics but also in chemistry, meteorolo­ gy, biology and many areas of engineering. Concerning questions in this context we recommend the reader to the monographs by HAKEN (197B), and EBElING, FEISTEl (1982). An overview of the problems of recent interest in this field is given in the Proceedings of the Third International Conference on Irreversible Processes and Dissipative Structures, edited by EBElING and Ul8RICHT (1986).

1. Introduction.- 1.1. Types and Classification of Phase Transitions.- 1.2. Thermodynamic and Experimental Conditions for Supersaturated Vapour States.- 1.3. Outline of Classical Nucleation Theory.- 1.3.1. The Classical Droplet Model.- 1.3.2. Kinetic Assumptions of Classical Nucleation Theory.- 1.3.3. Modifications of Classical Nucleation Theory.- 1.4. Nucleation in a Lattice Gas Model.- 2. Thermodynamics of Heterogeneous Systems.- 2.1. Thermodynamic Premises of Classical Nucleation Theory.- 2.2. Gibbs’ Theory of Heterogeneous Systems.- 2.3. Curvature Dependence of Surface Tension.- 2.4. Heterogeneous Systems in Non-Equilibrium States and the Principle of Inner Equilibrium.- 3. Thermodynamics and Nucleation in Finite Systems.- 3.1. The Work of Formation of Clusters.- 3.2. Equilibrium States and the Conditions for Stability of the Clusters.- 3.3. Critical Thermodynamic Parameters for Nucleation in Finite Systems.- 3.4. The Work of Formation of Critical Clusters.- 3.5. Parameters of the Critical Cluster in Dependence on the System Size.- 3.6. Formation of a Droplet Ensemble in Finite Systems.- 4. Kinetics of Phase Transitions in Finite Systems — A Stochastic Approach.- 4.1. Free Energy of the Cluster Distribution.- 4.2. Kinetic Assumptions and Master Equation.- 4.3. Results of Computer Simulations.- 4.3.1. Stochastic Dynamics Technique.- 4.3.2. Evolution of a Single Cluster.- 4.3.3. Evolution of the Cluster Distribution.- 4.4. Probability Distribution and Mean First Passage Time.- 4.5. Mean Values for the Number of Clusters — Fokker-Planck Equation.- 5. Kinetics of Growth of a New Phase — A Deterministic Description.- 5.1. General Scenario of First-Order Phase Transition in Finite Systems.- 5.2. Nucleation in Finite Systems — The Quasi-Steady-State-Approximation.- 5.3. Deterministic Growth Equations.- 5.3.1. Diffusion Equation Approach.- 5.3.2. Derivation of a General Growth Equation for Clusters of a New Phase.- 5.4. Simultaneous Description of Nucleation and Growth.- 5.5. Curvature Dependence of Surface Tension and the Scenario of First-Order Phase Transitions.- 5.6. Further Applications.- 6. Theory of Ostwald Ripening.- 6.1. Basic Equations.- 6.2. The Lifshitz-Slyozov Theory.- 6.3. Thermodynamic Aspects of Ostwald Ripening in Solids and Liquid Solutions.- 6.4. A New Method of Kinetic Description of Ostwald Ripening.- 6.5. Ostwald Ripening and the Relations to the Theory of Self-Organization.- 7. Growth of Bubbles in Finite Systems.- 7.1. The Model.- 7.2. Thermodynamic Analysis.- 7.3. Kinetic Description of Nucleation and Growth of Bubbles.- 7.4. Applications to Liquid-Gas Solutions and Multicomponent Systems.- 8. Nucleation and Growth in Elastic and Viscoelastic Media.- 8.1. Derivation of a Growth Equation for Clusters in Elastic Media.- 8.2. Models for the Calculation of Elastic Strains.- 8.2.1. Elastic Strains of Nabarro Type.- 8.2.2. Elastic Strains in Segregation Processes in Elastic Media.- 8.2.3. The Influence of Viscous Properties of the Matrix on the Development of Elastic Strains.- 8.3. Formation and Growth of Single Clusters in Elastic Media.- 8.4. Ostwald Ripening in Elastic and Viscoelastic Media.- References.